In this paper, the main purpose is to reveal what kind of qualitative dynamical
changes a continuous age-structured model may undergo as continuous reproduction is replaced with
an annual birth pulse. Using the discrete dynamical system determined by
the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility
and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical
flip bifurcation at the bifurcation as well as extensive analysis of dynamics in unstable
parameter regions. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic
dynamics, which implies that the dynamical behavior of the single species model with birth pulses
are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos.
This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows
for a period-doubling route to chaos. Finally, we discuss the effects of generation delay on stability of positive
equilibrium (or positive periodic solution), and show that generation delay is found
to act both as a destabilizing and a stabilizing effect.